Question : -
Abdul travelled
300
km by train and
200
km by taxi, it took him
5
hours
30
minutes. But it he travels
260
km by train and
240
km by taxi he takes
6
minutes longer. Find the speed of the train and that of the taxi.
solution: - Let the speed of train be
x
km/hr and speed of taxi be
y
km/hr.

We know,
T
i
m
e
=
D
i
s
t
a
n
c
e
S
p
e
e
d

5
hr
30
minutes
=
5
+
30
60
=
5
+
1
2
=
11
2
h
r
s

5
hr
36
minutes
=
5
+
36
60
=
5
+
6
10
=
28
5
h
r
s

From the given information, we have,

300
x
+
200
y
=
11
2
a
n
d
260
x
+
240
y
=
28
5


Putting
1
x
=
p
a
n
d
1
y
=
q
, we have

300
p
+
200
q
=
11
2
a
n
d
260
p
+
240
q
=
28
5


o
r
,
300
p
+
200
q
=
11
2

⇒
100
(
3
p
+
2
q
)
=
11
2

⇒
2
(
3
p
+
2
q
)
=
0.11

⇒
6
p
+
4
q
=
0.11....
(
i
)

A
l
s
o
,
260
p
+
240
q
=
28
5

⇒
20
(
13
p
+
12
q
)
=
28
5

⇒
13
p
+
12
q
=
0.28

⇒
12
q
=
0.28
−
13
p

⇒
q
=
0.28
−
13
p
12
.
.
.
.
(
i
i
)

Substituting equation (ii) in equation (i), we get,

6
p
+
4
q
=
0.11

⇒
6
p
+
4
(
0.28
−
13
p
12
)
=
0.11

⇒
6
p
+
0.28
3
−
13
p
3
=
0.11

⇒
5
p
3
=
0.11
−
0.28
3

⇒
5
p
=
0.33
−
0.28

⇒
p
=
0.05
5
=
1
100

Substituting
p
=
1
100
in equation (ii), we get,

q
=
0.28
−
13
p
12
=
0.28
−
13
×
1
100
12
=
0.28
−
0.13
12
=
0.15
12
=
1
80

p
=
1
x
=
1
100
⇒
x
=
100

q
=
1
y
=
1
80
⇒
y
=
80

Thus, speed of train
=
x
=
100
km/hr and speed of taxi
=
y
=
80
km/hr.